Analysis Seminar

Chelkak, Laslier, and Russkikh introduce a new type of graph embedding called a t-embedding, and use it to prove the convergence of dimer model height fluctuations to a Gaussian Free Field in a naturally associated metric, under certain technical assumptions. Building on a work of Chelkak and Ramassamy, we study the properties of t-embeddings of uniform Aztec diamond graphs, and in particular utilize the integrability of the "shuffling algorithm" on these graphs to provide a precise asymptotic analysis of t-embeddings, and in particular verify the validity of the technical assumptions required for convergence.